Constructing a Model of the Axis Form in a S-shaped Riser of a Cultivator Paw
Year: 2025
Type: article
Abstract: When cultivating the soil, the cultivator foot is subjected to a force of resistance to its movement. It is of variable magnitude and causes a moment of force applied to the foot riser. Under the action of the moment, the elastic axis of the riser changes its shape. This affects the position of the foot in the soil. The shape of an S-shaped riser is considered, the elastic axis of which consists of two arcs of circles of the same radius. During the operation of the cultivator, one part of the riser bends, increasing the curvature of the elastic axis, and the other, on the contrary, unbends, i.e. its curvature decreases. The modeling of the shape of the elastic axis of the foot riser is based on the position of the theory of resistance of materials, according to which the curvature of the elastic axis of a cantilevered clamped strip is directly proportional to the applied moment and inversely proportional to its stiffness. If the shape of the cross-section of the riser along its entire length is unchanged and the properties of the metal are also the same, then the stiffness is constant. For small deflections of the strip, the linear bending theory is used, but the deflections in the riser are significant, so for this case, the nonlinear theory is used. In this case, it is taken into account that the elastic axis of the riser already has an initial curvature. If a cantilevered straight strip is bent by a force applied perpendicular to its free end, the strip will bend. When it is deformed, the force remains perpendicular to the end of the strip, although in a fixed coordinate system it changes its direction. Such a force is called a follower. When the cultivator is working, a force appears that is applied to the paw. The component of this force perpendicular to the end of the riser and transmitted to it from the paw will be considered as a follower. To model the shape of the elastic axis of the S-shaped riser of the paw, the deformation of the arcs of circles that form this paw was separately calculated. The moment of force at the current point of the elastic axis of the riser was calculated as the product of the following force applied to the riser at the point of attachment to the leg, by a distance that is the length of the elastic axis from this to the current point on the riser. Numerical integration methods were used to find the shape of the deformed elastic axes of both parts of the riser. Then they were combined into one whole and the deformed elastic axis of the S-shaped riser was obtained.
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408205125